三角函數(shù)的圖像和性質(zhì)知識(shí)點(diǎn)及例題講解

1、1三角函數(shù)的圖像和性質(zhì)三角函數(shù)的圖像和性質(zhì)1、用五點(diǎn)法作正弦函數(shù)和余弦函數(shù)的簡圖（描點(diǎn)法）：正弦函數(shù)y=sinx，x∈[0，2π]的圖象中，五個(gè)關(guān)鍵點(diǎn)是：(00)(1)(?0)(1)(2?0)2?23?余弦函數(shù)y=cosxx?[02?]的圖像中，五個(gè)關(guān)鍵點(diǎn)是：(01)(0)(?1)(0)(2?1)2?23?2、正弦函數(shù)、余弦函數(shù)和正切函數(shù)的圖象與性質(zhì)：sinyx?cosyx?tanyx?圖象定義域RR2xxkk????????????值

2、域??11???11?R最值當(dāng)時(shí)，22xk????；當(dāng)max1y?22xk????時(shí)，min1y??當(dāng)時(shí)，2xk??；當(dāng)max1y?2xk????時(shí)，min1y??既無最大值也無最小值周期性2?2??奇偶性奇函數(shù)偶函數(shù)奇函數(shù)單調(diào)性在2222kk????????????上是增函數(shù)；在32222kk????????????上是減函數(shù)在上是增函??22kk????數(shù)；在上是減函??22kk????數(shù)在22kk????????????上是增函數(shù)

3、對(duì)稱性對(duì)稱中心??0k?對(duì)稱中心02k?????????對(duì)稱中心02k???????函數(shù)性質(zhì)3例5求函數(shù)的單調(diào)區(qū)間sin(2)3yx???例不求值，比較大小奎屯王新敞新疆(1)sin(－)、sin(－)；(2)cos(－)、cos(－)18?10?523?417?解：(1)∵－＜－＜－＜(2)cos(－)＝cos＝cos2?10?18?2?523?523?53?且函數(shù)y＝sinx，x∈［－，］是增函數(shù)奎屯王新敞新疆cos(－)＝cos＝

4、cos2?2?417?417?4?∴sin(－)＜sin(－)∵0＜＜＜π10?18?4?53?即sin(－)－sin(－)＞0且函數(shù)y＝cosx，x∈［0，π］是減函數(shù)18?10?∴cos＜cos53?4?即cos－cos＜053?4?∴cos(－)－cos(－)＜0523?417?4、函數(shù)的圖像：????sin00yx????A?A??（1）函數(shù)的有關(guān)概念：????sin00yx????A?A??①振幅：；②周期：；③頻率：；④相位